Question

numarul N=3^2011+2*3^2010+3^2009+3^2008 este patrat perfect

Answer 1

3²°¹¹+2*3²°¹°+3²°°⁹+3²°°⁸=3²°°⁸x(3³+2*3²+3+1)=3²°°⁸x(27+18+3+1)=3²°°⁸x49=(3¹°°⁴)²x7²
produs de doua patrate perfecta da patrat perfect

Answer 2

$3^{2011} +2* 3^{2010} +3^{2009} + 3^{2008} =3^{2008}( 3^{3}+2* 3^{2}+ 3+1)$=$3^{2008}(27+18+4)=3^{2008}*49=3^{2008} *7^{2} =(3^{1004}*7)^2$ => N pp